Strange you should ask. I took my cabin cushions out two days ago and was wondering how to clean them. One option was to remove the covers and wash them. I decided against that for several reasons. I then looked at upholstery cleaners, spray types but there were so many warnings about not using on certain fabrics, I nixed that idea also.
So last night I gave them a light scrub with water and Murphy's oil soap. Most of the dirt scrubbed off. This morning, after they dried, I gave them a treatment with 303 aerospace fabric treatment (not the 303 protectorant). This gives a water proofing coat that repels stains.
Note that 303 makes a fabric cleaner also and that might have been worth a shot if i were near a place to buy it.